Milan have been one of Europe's busiest clubs in the transfer window, bringing in 10 new players including Italy defender Leonardo Bonucci and Portugal striker Andre Silva, while handing a bumper new contract to goalkeeper Gianluigi Donnarumma.
The overhaul of Vincenzo Montella's squad is intended to boost Milan's chances of qualifying for the Champions League, but Pallotta questioned the club's strategy following the takeover from Li Yonghong's company Rossoneri Sport Investment Lux – though he later admitted some of his information may have been incorrect.
"UEFA, in terms of Financial Fair Play, has been a complete ****show for us," Pallotta told Sirius XM FC on Thursday.
"We should be the poster boy for turning things around from the previous ownership. When you relate it to AC Milan, I have no idea what is going on there. It makes zero sense.
"The amount of spending - they didn't have the money in the first place to buy the club, as they borrowed almost €300million from some people that I know in London, at a pretty high interest rate.
"They are spending - or at least making some significant down-payments - for players and they're going to have to pay the piper at some point down the road.
"They say it's about qualifying for the Champions League, but that won't be enough. When the salary seems about equal to the revenues, I don't know what the heck is going on."
But Milan CEO Fassone rejected Pallotta's suggestion their spending is unsustainable, branding such comments inaccurate.
"I was stunned when I read these words this morning," Fassone said in a video posted on Milan's Facebook page on Friday. "For one thing, because of the style. It's unusual, at least in Italy, for a club to attack another one in such a direct way. Secondly for the inaccuracy of his words.
"We all know that in order to purchase a club you need a financial leverage. Moreover, he's talking about figures that are inaccurate.
"We have issued a bond which is entirely destined to finance our transfer campaign for this summer and we are currently well below using up this bond.
"There are long-term plans that we have submitted to a board of directors which should be a guarantee and we have submitted to UEFA a voluntary agreement which everyone knows about, it's public and should president Pallotta wish to see it, I am absolutely open to this opportunity.
"The club's €120million debt compared to the club's revenues is in percentage way better than Roma's."
After Fassone's response, Pallotta issued a statement to Milan via the Roma website.
"I apologise if I used some incorrect information," Roma's president said. "I care a lot about Italian football returning to the top and in that respect, I expect that all the clubs can contribute to a stronger and more sustainable league, like we are doing at Roma.
"I wish Milan and the new owners all the best and look forward to their management and new owners working with all of us to be a key part of Serie A's growth."